Dear students and parents,

Here is the file of 20 SAT Math Sample questions to practice at home this weekend.

https://collegereadiness.collegeboard.org/pdf/official-sat-study-guide-sample-math-questions-multiple-choice.pdf

Take care in this special season!

Best,

Lijia

SAT-Math 2020 Spring Week 1:  Linear Models

Welcome new friend Abby!

This is the first class in the Spring Semester. By the end of June, we will go through all the topics including linear/quadratics, number theory foundation (synthetic division, complex numbers, absolute value), geometry (angles, triangles, circles, and volumes), trigonometry, probability, statistics, and reading data.

Lesson Review:

1. Comments & corrections on 2019 Fall Final Term

• When the coefficients of each term are equal, we can say the left and right parts of an equation are equal. (Section 3, Q10, and Section 4, Q16)
• The root square should be non-negative (Section 3, Q15)
• Read every keyword carefully. Know which data you should look into. (Section 4, Q9)
• Pythagorean Triples (3,4,5), (5,12,13), (7,24,25) and so on.
• …

2. Chapter 14: Interpreting Linear Models

• Understanding the meanings/applications of “slope” (rate of change) and ”y-intercept” (the value of the function when x=0).

Homework:

1. Corrections of Final Exam Paper

2. Chapter 14 Exercise (Page 113-116)

Other Resources:

https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/gtp–praxis-math–lessons–statistics-and-probability/a/gtp–praxis-math–article–interpreting-linear-models–lesson

No school next Sunday. Happy Lunar New Year! See you on 2/2！

今天的考试Section 4在复印试题的时候发生“意外”，打印机误将2张纸一起卷进去，导致中间2面的试题没有复印，这样全班人20-25题都没有做，直到李老师批改试卷的时候才发觉！所以下周日上课会抽出5分钟时间给大家补做这5题！抱歉发生这样的乌龙~~

试卷都已经批好，错题也已经录入我的小数据库。这次期末比期中考试难了一些，我们会在下周挑选典型错题重点讲解。

下周会开始新的一章，Chapter 14: Interpreting Linear Models. 请大家记得带上课本与试卷。

另外，我们把Teaching Schedule做了微调，原定3.15的期中考试推迟到3月29日。这样保证前后半个学期的课时数相对均衡。具体详见：

我们下周见！（还未注册春季学期课程的家长请勿错过1月19日的报名缴费日期^_^）

SAT-Math Week 14: Lines

Lesson Review:

1. forms of linear equations
2. Slope
3. Parallel lines and perpendicular lines
4. vertical line and horizontal line

Homework: Chapter 13 Exercise (Page 108-110)

Other Resources:

• https://www.mathsisfun.com/algebra/linear-equations.html
• https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs
• http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
• https://www.mathplanet.com/education/algebra-1/how-to-solve-linear-equations

Something Else:

Next week we are going to have our final exam. Please remember to bring your calculator. See you soon!

Lesson Review:

Inequality signs:

Properties of inequality:

Inequalities on a number line:

Solving inequalities:

Graph linear inequalities:

Graph system of linear inequalities (find the overlapping area):

Solve quadratic inequalities:

Extra Resource:

https://www.mathsisfun.com/algebra/inequality-solving.html

https://mathbitsnotebook.com/Algebra1/Inequalities/IQinequalities.html

Homework:

Page 88-92: Chapter 11 Exercise (16 problems)

Something Else:

*I will be back to China from 12/10 to 12/27. Next Sunday (12/15) we will have Mr. Xu (the teacher of AoPS: Precalculus) to teach Ch.12 Word Problems. Thank you, Mr. Xu!

There is no school on 12/22 and 12/29. Merry Christmas and Happy New Year, everyone! See you on 1/5/2020 for our last class before the final exam on 1/12!

Lesson Review:

There are 3 types of solutions when it comes to solving systems of equations. Either you will get:

• One solution (which will be given in an ordered pair) – the two lines cross each other in ONE place (this intersect is the solution). Different slopes.
• No solution – the two lines are parallel to each other and never cross. They have the same slope but different y-intercepts.
• Infinite solutions – the two lines are directly on top of each other (colinear). Since there are infinite points where the two lines cross, there are infinite solutions. They have the same slope and the same y-intercept.

Systems of equations can be solved by:

• Graphing Method
• Substitution Method
• Elimination Method
• Matrix Method / Cramer’s Rule (not discussed in this course)

Homework: Page 77-81, Ex 1-23

Additional Resources:

• https://www.mathwithdabit.com/in-class-lab-solving-systems.html
• https://www.youtube.com/watch?v=nok99JOhcjo

No School next week. Enjoy the holiday😊

SAT Math Week 10: More Equation Solving Strategies

Lesson Review:
Today we discussed Chapter 8 Exercise and went through Chapter 9: More Equation Solving Strategies.

1) Matching coefficients
2) Clearing denominators

*Note that a lot of SAT problems will include some conditions such as x>0 or x<0, to eliminate one of the solutions. Read the questions carefully.

*For some long questions, you do not need to read every single word. Catch the keywords, focus on the formula or equations, you will save time and reduce the working load of your brain!

Homework:
1)Page 66-67, Ex 1-12
2)Bonus Problem 13-17

Extra Resource:
https://www.math.utah.edu/~macarthu/fall08/math1010/EquationSolvingStrategies.pdf

https://blog.prepscholar.com/single-variable-equations-algebra-act-math-strategies

Next week we are going to solve systems of equations! See you soon!

Welcome our new friend, Tina!

Flexibility Assessment:
Thanks to everyone for participating in the pilot Flexibility Assessment from Harvard Graduate School of Education. Your feedback will help to revise this assessment. This study will be carried out in Finland, Sweden, Spain, America, and China. We learned that for some problems, there are some “innovative strategies”. Be familiar with the properties and principles in math, you can solve problems faster, and better:)

I was deeply impressed that several of you can solve many (even all) of the problems in an innovative way in Part I (the first trial). Good job! Please remember to apply these strategies in your SAT tests to save time 😛

Responding to the feedback from Emma’s mom, in the following lessons, I would love to share some strategies to 1) read long questions 2) reduce the workload of calculating during the SAT test.

Lesson Review:
We discussed Page 57: Ex(3n +1) and went through the 12 example problems in Chapter 8. Some useful techniques in dealing with equations include but not limited to:
1) combine like terms
2) square and square root
3) cross-multiply (fractions)
4) factoring
5) treat complicated expressions as one unit
6) solve for expressions, rather than any one variable
7) Guess and check

Homework:
Page 58-62, Ex 1-24
(everyone picks 2 problems that you feel most challenged and would like us to explain in class, and label them on your textbook)
(everyone prepares to explain on board in class！We will do the shuffling cards again:P）

We will explore more equation solving strategies (Chapter 9) next week. See you then!

Lesson Review:

1. Midterm Exam Paper Review
2. Page 57, Problem 3n: Isolate the variables
3. Chapter 7: Constructing Models
   Note the difference between linear function, quadratic function, and exponential functions;
   Note the increasing/decreasing (the slopes, the trend of lines)
   Note the rate of change (quickly: steeper lines, |slope|is greater; slowly: |slope| is smaller). || means absolute values.

Homework:

1. Midterm Exam Paper Correction (Use different colors)
2. Page 57, Problem 3n+1: Isolate the variables
3. Chapter 7: Constructing Models Chapter Exercise (Page 47-49)

Look forward to seeing you on 11/10.